A Healthier You Is Just A Few Equations Away

Written by: Oscar E. Fernandez, Associate Professor of Mathematics at Wellesley College

How many calories should you eat each day? What proportion should come from carbohydrates, or protein? How can we improve our health through diets based on research findings?

You might be surprised to find that we can answer all of these questions using math. Indeed, mathematics is at the heart of nutrition and health research. Scientists in these fields often use math to analyze the results from their experiments and clinical trials. Based on decades of research (and yes, math), scientists have developed a handful of formulas that have been proven to improve your health (and even help you lose weight!).

So, back to our first question: How many calories should we eat each day? Let’s find out...

Each of us has a “total daily energy expenditure” (TDEE), the total number of calories your body burns each day. Theoretically, if you consume more calories than your TDEE, you will gain weight. If you consume less, you will lose weight. Eat exactly your TDEE in calories and you won’t gain or lose weight.

“Great! So how do I calculate my TDEE?” I hear you saying. Good question. Here’s a preliminary answer:

TDEE = RMR + CBE + DIT (1)

Here’s what the acronyms on the right-hand side of the equation mean.

RMR: Your resting metabolic rate, roughly defined as the number of calories your body burns while awake and at rest

CBE: The calories you burned during the day exercising (including walking)

DIT: Your diet’s diet-induced thermogenesis, which quantifies what percentage of calories from dietary fat, protein, and carbohydrates are left over for your body to use after you ingest those calories

So, in order to calculate TDEE, we need to calculate each of these three components. This requires very precise knowledge of your daily activities, for example: what exercises you did, how many minutes you spent doing them, what foods you ate, and how much protein, carbohydrates, and dietary fat these foods contained. Luckily, nutrition scientists have developed a simpler formula that takes all of these factors into account:

TDEE = RMR(Activity Factor) + 0.1C. (2)

Here C is how many calories you eat each day, and the “Activity Factor” (below) estimates the calories you burn through exercise:

Level of Activity

Activity Factor

Little to no physical activity

1.2

Light-intensity exercise 1-3 days/week

1.4

Moderate-intensity exercise 3-5 days/week

1.5

Moderate- to vigorous-intensity exercise 6-7 days/week

1.7

Vigorous daily training

1.9

As an example, picture a tall young man named Alberto. Suppose his RMR is 2,000 calories, that he eats 2,100 calories a day, and that his Activity Factor is 1.2. Alberto’s TDEE estimate from (2) would then be

TDEE = 2,000(1.2) + 0.1(2,100) = 2,610.

Since Alberto’s caloric intake (2,100) is lower than his TDEE, in theory, Alberto would lose weight if he kept eating and exercising as he is currently doing.

Formula (2) is certainly more user-friendly than formula (1). But in either case we still need to know the RMR number. Luckily, RMR is one of the most studied components of TDEE, and there are several fairly accurate equations for it that only require your weight, height, age, and sex as inputs. I’ve created a free online RMR calculator to make the calculation easier: Resting Metabolic Heart Rate. In addition, I’ve also created a TDEE calculator (based on equation (2)) to help you estimate your TDEE: Total Daily Energy Expenditure.

I hope this short tour of nutrition science has helped you see that mathematics can be empowering, life-changing, and personally relevant. I encourage you to continue exploring the subject and discovering the hidden math all around you. You can learn more this summer in the Wellesley Pre-College Exploratory Workshop: Mathematics of Metabolism, Diet and Health.